Abstract: Asynchronous Computing for Partial Differential Equations at Extreme Scales

Advances in computing technology have made numerical simulations an indispensable research tool in the pursuit of understanding real life problems. Due to their complexity, these simulations demand massive computations with extreme levels of parallelism. At extreme scales, communication between processors could take up a substantial amount of time. This results in substantial waste in computing cycles, as processors remain idle for most of the time. We investigate a novel approach based on widely used finite-difference schemes in which computations are carried out in an asynchronous fashion - synchronization among cores is not enforced and computations proceed regardless of the status of messages. This drastically reduces idle times resulting in much larger computation rates and scalability. However, stability, consistency and accuracy have to be shown in order for these schemes to be viable. This is done through mathematical theory and numerical simulations. Results are used to design new numerical schemes robust to asynchronicity.